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- W2078118679 abstract "A conjecture due to Honda predicts that given any abelian variety over a number field K, all of its quadratic twists (or twists of a fixed order in general) have bounded Mordell-Weil rank. About 15 years ago, Rubin and Silverberg obtained an analytic criterion for Honda’s conjecture for a family of quadratic twists of an elliptic curve defined over the field of rational numbers. In this paper, we consider this problem over number fields. We will prove that the existence of a uniform upper bound for the ranks of elliptic curves in this family is equivalent to the convergence of a certain infinite series. This result extends the work of Rubin and Silverberg over ℚ." @default.
- W2078118679 created "2016-06-24" @default.
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- W2078118679 date "2014-12-01" @default.
- W2078118679 modified "2023-10-16" @default.
- W2078118679 title "On the ranks of elliptic curves in families of quadratic twists over number fields" @default.
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- W2078118679 doi "https://doi.org/10.1007/s10587-014-0149-y" @default.
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